Navigation satellite system positioning involving the generation of receiver-specific or receiver-type-specific correction information

ABSTRACT

The invention relates to methods, apparatuses and computer programs for generating receiver-specific correction information for correcting pseudorange observations. The method comprises: receiving raw observations obtained by the NSS receiver observing NSS multiple frequency signals from a plurality of NSS satellites over multiple epochs; obtaining precise satellite information on: (i) the orbit position of each of the satellites, (ii) a clock offset of each of the satellites, and (iii) a set of biases associated with each of the satellites; estimating ambiguities in the carrier phase of the received raw observations, using the precise satellite information, or information derived therefrom; computing combination values based on the received raw observations together with the estimated ambiguities, to cancel out the effects of the geometry, the effects of the clocks, troposphere and ionosphere; and generating the correction information per satellite, based on the computed combination values.

FIELD OF TECHNOLOGY

The invention relates to global or regional navigation satellite systems(NSS) position estimation methods, devices and computer programs. Thefields of application of the methods, devices and computer programsinclude, but are not limited to, navigation, map-making, land surveying,civil engineering, agriculture, disaster prevention and relief, andscientific research.

BACKGROUND

Navigation satellite systems (NSS) include both global navigationsatellite systems (GNSS) and regional navigation satellite systems(RNSS), such as the Global Positioning System (GPS) (United States),GLONASS (Russia), Galileo (Europe), BeiDou (China), QZSS (Japan), andthe Indian Regional Navigational Satellite System (IRNSS) (systems inuse or in development). A NSS typically uses a plurality of satellitesorbiting the Earth. The plurality of satellites forms a constellation ofsatellites. A NSS receiver detects a code modulated on anelectromagnetic signal broadcast by a satellite. The code is also calleda ranging code. Code detection includes comparing the bit sequencemodulated on the broadcasted signal with a receiver-side version of thecode to be detected. Based on the detection of the time of arrival ofthe code for each of a series of the satellites, the NSS receiverestimates its position. Positioning includes, but is not limited to,geolocation, i.e. the positioning on the surface of the Earth.

An overview of GPS, GLONASS and Galileo is provided for instance insections 9, 10 and 11 of Hofmann-Wellenhof B., et al., GNSS, GlobalNavigation Satellite Systems, GPS, GLONASS, Galileo, & more,Springer-Verlag Wien, 2008, (hereinafter referred to as “reference[1]”).

Positioning using NSS signal codes provides a limited accuracy, notablydue to the distortion the code is subject to upon transmission throughthe atmosphere. For instance, the GPS includes the transmission of acoarse/acquisition (C/A) code at 1575.45 MHz, the so-called L1frequency. This code is freely available to the public, whereas thePrecise (P) code is reserved for military applications. The accuracy ofcode-based positioning using the GPS C/A code is approximately 15meters, when taking into account both the electronic uncertaintyassociated with the detection of the C/A code (electronic detection ofthe time of arrival of the pseudorandom code) and other errors includingthose caused by ionospheric and tropospheric effects, ephemeris errors,satellite clock errors and multipath propagation.

An alternative to positioning based on the detection of a code ispositioning based on carrier phase measurements. In this alternativeapproach or additional approach (ranging codes and carrier phases can beused together for positioning), the carrier phase of the NSS signaltransmitted from the NSS satellite is detected, not (or not only) thecode modulated on the signal transmitted from the satellite.

The approach based on carrier phase measurements has the potential toprovide much greater position precision, i.e. up to centimetre-level oreven millimetre-level precision, compared to the code-based approach.The reason may be intuitively understood as follows. The code, such asthe GPS C/A code on the L1 band, is much longer than one cycle of thecarrier on which the code is modulated. The position resolution maytherefore be viewed as greater for carrier phase detection than for codedetection.

However, in the process of estimating the position based on carrierphase measurements, the carrier phases are ambiguous by an unknownnumber of cycles. The phase of a received signal can be determined, butthe number of cycles cannot be directly determined in an unambiguousmanner. This is the so-called “integer ambiguity problem”, “integerambiguity resolution problem” or “phase ambiguity resolution problem”,which may be solved to yield the so-called fixed solution.

GNSS observation equations for code observations and for carrier phaseobservations are for instance provided in reference [1], section 5. Anintroduction to the GNSS integer ambiguity resolution problem, and itsconventional solutions, is provided in reference [1], section 7.2. Theskilled person will recognize that the same or similar principles applyto RNSS systems.

The main GNSS observables are therefore the carrier phase and code(pseudorange), the former being much more precise than the latter, butambiguous. These observables basically enable a user to obtain thegeometric distance from the receiver to the satellite. With knownsatellite position and satellite clock error, the receiver position canbe estimated.

Due to different tracking and multipath mitigation technology used bydifferent receivers or different generations of receiver board,significant receiver-dependent satellite code biases exist amongdifferent receiver models.

Yamada, H., Takasu, T., Kubo, N., Yasuda, A., Evaluation and calibrationof receiver inter-channel biases for RTK-GPS/GLONASS, 23rd internationaltechnical meeting of the satellite division of the institute ofnavigation, Portland, Oreg., USA (2010) (hereinafter referred to as“reference [2]”), found that, for the GLONASS system, the biases mayamount to several meters in the L1/L2 band.

Reussner, N., Wanninger, L. GLONASS Inter-frequency Biases and TheirEffects on RTK and PPP Carrier-phase Ambiguity Resolution, Proc. of IONGNSS 2011, Portland, Oreg., USA (hereinafter referred to as “reference[3]”), found that the ionosphere-free GLONASS code biases are presentalso for same receiver type baselines and may amount to several meters.Furthermore, these biases cannot be modelled as a function of theGLONASS channel number k (for more details in that respect, see forexample “GLONASS Interface Control Document, Navigational radiosignal Inbands L1, L2”, Edition 5.1, Moscow, 2008, section 3.3.1.1: “Frequencyplan”). Finally, there is evidence that, even for antipodal GLONASSsatellites (same channel number k), the biases may reach the meterlevel. The method disclosed in reference [3] does not allow theestimation of the L1 and L2 biases separately, but only theionosphere-free combination of such biases.

The effect of the receiver code biases per satellite is apparent whenthe double-difference multipath combination residuals are computed, asshown in FIG. 2.

The existence of the code biases degrades the positioning accuracy insingle-receiver and differential mode. It is thus useful to remove thesebiases through a proper calibration process. The proper calibration ofsuch biases improves not only the NSS positioning but also the estimatesof the receiver and satellites clocks and the medium-induced delays(troposphere and ionosphere). For the end user, this may result in abetter precision of the user receiver coordinates achieved in a shortertime span.

A typical calibration process is to use a zero-baseline setup (seereference [2], and Al-Shaery, A., Zhang, S., Rizos, C., An enhancedcalibration method of GLONASS inter-channel bias for GNSS RTK, GPSSolutions (2013) 17:165-173, hereinafter referred to as “reference[4]”), where at least two receivers are connected to the same physicalantenna, and receivers (of the same type) are calibrated with respect toreference receivers (of the same type). With zero-baseline calibration,the code bias of each satellite can be derived from one receiverrelative to a reference receiver. This approach is very accurate as themultipath, troposphere and ionosphere effects are cancelled out. Thedrawback is that the receivers need to be connected to the same antenna.Additional effects due to the antenna and the antenna cable are notaccounted for. A zero-baseline setup is schematically illustrated inFIG. 8. The square represents the antenna, and the two rectanglesrepresent the receiver to be calibrated and the reference receiver,respectively.

In some cases, this setup can be substituted by a short-baseline setup.The short-baseline (few meters) calibration reduces the medium-dependenterrors, while the geometry is removed by the a-priori knowledge of theantenna coordinates and satellite positions. The antenna effect isaccounted for in the short-baseline calibration setup, so that theapproach is more suitable to calibrate smart antennas (receiver andantenna integrated in the same housing) than zero-baseline calibration.A short-baseline setup is schematically illustrated in FIG. 9.

There is a constant need for improving the implementation of positioningsystems based notably on GNSS (or RNSS) carrier phase measurements, toobtain a precise estimation of the receiver position, in particular inview of the problems associated with the above-mentioned calibrationapproaches.

SUMMARY

The present invention aims at addressing the above-mentioned need. Theinvention includes methods, apparatuses, computer programs, computerprogram products and storage mediums as defined in the independentclaims. Particular embodiments are defined in the dependent claims.

In one embodiment of the invention, a method is provided for generatingcorrection information associated with at least one global or regionalnavigation satellite system receiver (NSS) receiver, wherein thecorrection information comprises information for correcting pseudorangeobservations. The pseudorange observations are useful for determining aposition of the at least one NSS receiver. The method comprises:receiving raw observations obtained by one of the at least one NSSreceiver observing NSS multiple frequency signals from a plurality ofNSS satellites over multiple epochs; obtaining information, hereinafterreferred to as “precise satellite information”, on: (i) the orbitposition of each one of the plurality of NSS satellites, (ii) a clockoffset of each one of the plurality of NSS satellites, and (iii) a setof biases associated with each one of the plurality of NSS satellites,or obtaining information derived from the precise satellite information;estimating ambiguities in the carrier phase of the received rawobservations, using the precise satellite information, or using theinformation derived therefrom; computing combination values based on thereceived raw observations together with the estimated ambiguities, tocancel out the effects of the satellite motion relative to the at leastone NSS receiver, the effects of the clocks, the effects of thetroposphere and the effects of the ionosphere; and generating thecorrection information per satellite, based on the computed combinationvalues.

The method enables the processing of NSS raw observations to estimateNSS receiver code biases by making use of the precise satelliteinformation, or information derived therefrom, which may for example bein the form of a correction data stream generated based on a network ofreference stations. The method typically does not require the use ofdedicated equipment (i.e., the use of dedicated hardware) forcalibration, as required in the above-discussed zero- and short-baselineapproaches, and the method does not require a spatial constraint to beapplied. The precise satellite information, or information derivedtherefrom, may be regarded as acting as a virtual reference in thecalibration process. The method enables to improve the positioning ofthe NSS receiver(s), to improve the ambiguity resolution, and thusreducing the convergence time needed for a carrier-phase-based preciseposition estimate, to improve the precision of the estimates of nuisanceparameters (tropospheric delay, ionospheric delay and receiver clockoffset from an NSS time), and/or to detect a hardware problem in an NSSreceiver.

In one embodiment, a plurality of receivers of the same or similar typemay receive, and therefore benefit from, the same correctioninformation.

In one embodiment, the generated correction information comprisesestimated receiver code biases per satellite.

The invention also relates, in one embodiment, to an apparatusconfigured for generating correction information associated with atleast one NSS receiver, wherein the correction information comprisesinformation for correcting pseudorange observations, and the pseudorangeobservations are useful for determining a position of the at least oneNSS receiver. The apparatus comprises a first unit referred to as “rawobservations receiving unit”, a second unit, referred to as “precisesatellite information obtaining unit”, a third unit, referred to as“ambiguities estimating unit”, a fourth unit, referred to as“combination values computing unit”, and a fifth unit, referred to as“correction information generating unit”. The raw observations receivingunit is configured for receiving raw observations obtained by one of theat least one NSS receiver observing NSS multiple frequency signals froma plurality of NSS satellites over multiple epochs. The precisesatellite information obtaining unit is configured for obtaining precisesatellite information on: (i) the orbit position of each one of theplurality of NSS satellites, (ii) a clock offset of each one of theplurality of NSS satellites, and (iii) a set of biases associated witheach one of the plurality of NSS satellites, or configured for obtaininginformation derived from the precise satellite information. Theambiguities estimating unit is configured for estimating ambiguities inthe carrier phase of the received raw observations, using the precisesatellite information, or using the information derived therefrom. Thecombination values computing unit is configured for computingcombination values based on the received raw observations together withthe estimated ambiguities, to cancel out the effects of the satellitemotion relative to the at least one NSS receiver, the effects of theclocks, the effects of the troposphere and the effects of theionosphere. Finally, the correction information generating unit isconfigured for generating the correction information per satellite,based on the computed combination values.

The invention also relates, in some embodiments, to computer programs,computer program products, and storage mediums for storing such computerprograms, comprising computer-executable instructions for carrying out,when executed on a computer such as a NSS receiver or on anotherapparatus, any one of the above-mentioned methods.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the present invention shall now be described, inconjunction with the appended drawings in which:

FIG. 1 a is a flowchart of a method in one embodiment of the invention;

FIG. 1 b is a flowchart of a method in one embodiment of the invention,being a more specific embodiment than FIG. 1 a in that, in step s30, theambiguities are set to integer values and thus regarded as resolved;

FIG. 1 c is a flowchart of a method in one embodiment of the invention,being a more specific embodiment than FIG. 1 b in that it involves thegeneration of synthetized base station observations;

FIG. 2 illustrates the effects of the receiver code biases per satelliteon the double-difference residuals of the multipath combination(GLONASS, L1CA; BEDF station, 15 Nov. 2013), where the mean biases forGLONASS 3 and 13, chosen as examples, are shown as solid and dottedlines;

FIG. 3 (with a scale reduced from FIG. 2) illustrates the effects of thereceiver code biases per satellite on the double-difference multipathcombination (GLONASS, L1CA; BEDF station, 15 Nov. 2013), when a methodaccording to one embodiment of the invention is used, where the meanbiases for GLONASS 3 and 13, chosen as examples, are shown as solid anddotted line, and reduced significantly in value;

FIG. 4 provides a comparison between the L1CA/L2PE GPS biases in metresestimated by a zero-baseline approach (black bars) and an embodiment ofthe method of the invention (white bars) (zero-baseline experiment inHöhenkirchen, Germany, day of year 149, 2013), confirming similar valuesbetween these methods;

FIG. 5 is the GLONASS counterpart of FIG. 4, i.e. FIG. 5 provides acomparison between the L1CA/L2CA GLONASS biases in metres estimated by azero-baseline approach (black bars) and an embodiment of the method ofthe invention (white bars) (zero-baseline experiment on Höhenkirchen,Germany, day of year 149, 2013), confirming similar values between thesemethods;

FIG. 6 shows the ambiguity fixing performance improvement for BEDFstation on day of the year 319, 2013;

FIG. 7 shows the wide-lane ambiguity fixing improvement for many networkstation identity codes using the “ambiguity fixing rate” (as apercentage) performance metric based on the Melbourne-Wübbenacombination with receiver code bias calibration compared to a situationwithout additional calibration (i.e., in addition to the calibrationvalues typically shipped with the receiver);

FIG. 8 shows a zero-baseline setup for the estimation of the receivercode biases per satellite, wherein two receivers are physicallyconnected to the same antenna, and wherein common mode effects due toantenna, cable, ionosphere, troposphere and satellite are cancelled outwhen single differences are computed;

FIG. 9 shows a short-baseline setup for the estimation of the receivercode biases per satellite, wherein two receivers are connected todifferent antennae, and wherein satellite biases and clock errors arecancelled out, antenna and cable are not cancelled, and ionosphere andtroposphere errors are mitigated to a level mostly dictated by thebaseline length;

FIG. 10 schematically illustrates an apparatus in one embodiment of theinvention; and

FIGS. 11 a to 11 e schematically illustrate five systems in embodimentsof the invention.

DETAILED DESCRIPTION

The present invention shall now be described in conjunction withspecific embodiments. The specific embodiments serve to provide theskilled person with a better understanding, but are not intended to inany way restrict the scope of the invention, which is defined byappended claims. In particular, the embodiments described independentlythroughout the description can be combined to form further embodimentsto the extent that they are not mutually exclusive.

Throughout the following detailed description, the abbreviation “GNSS”is used. The invention is, however, not limited to global navigationsatellite systems (GNSS) but also applies to regional navigationsatellite systems (RNSS). Thus, it is to be understood that eachoccurrence of “GNSS” in the following can be replaced by “RNSS” to formadditional embodiments of the invention.

In the following, it should also be understood that, when it ismentioned that the ambiguities are resolved or regarded as resolved, itis meant that an attempt is made to resolve the ambiguities, the outcomeof which will decide if an “ambiguity resolution” method or an“ambiguity reduction” method is employed, both methods being differentembodiments of the invention.

FIG. 1 a is a flowchart of a method according to one embodiment of theinvention. The method serves to estimate parameters which are derived atleast from GNSS signals and are useful to determine a position, such asthe position of a rover receiver or reference station, i.e. the positionof a NSS receiver of the same (or similar) type as the one receiving theraw observations. The NSS receiver(s) may be static or moving. Themethod may eventually lead to determining or estimating the roverposition or reference station position, i.e. the position of the NSSreceiver. The method may be performed by a receiver and/or a networknode.

The method involves generating correction information for thepositioning process. The correction information, or, in one embodiment,the receiver code bias, is computed (in steps s40 and s50) based on aprecise estimation of the satellite phase and code biases (see step s20)as well as on estimating the ambiguities (step s30). In such a way, thecontribution of the satellite biases may be directly removed from theobservations, while the medium-dependent delays may be eliminatedthrough the computation of combination values (step s40) such as, forexample, through the multipath combination. In particular, the methodcomprises the following steps.

In step s10, raw observations obtained by one of the NSS receiver(s)observing NSS multiple frequency signals from a plurality of NSSsatellites over multiple epochs is received (i.e., received by theapparatus carrying the method, and, if the NSS receiver carries out themethod, received internally within the NSS receiver). At least dualfrequency data is needed. In other words, in step s10, code pseudorangeand carrier phase observations are collected, i.e. obtained, by the NSSreceiver to be calibrated, and then distributed within the NSS receiverfor further processing or transferred to an apparatus in charge ofgenerating the correction information.

In step s20, precise satellite information, or information derivedtherefrom, is obtained. The precise satellite information comprisesinformation at least on: (i) the orbit position of each one of theplurality of NSS satellites, (ii) a clock offset of each one of theplurality of NSS satellites, and (iii) a set of biases associated witheach one of the plurality of NSS satellites, these set of biases beingassociated with the hardware delays within the respective satellites.The precise satellite information, or the information derived therefrom,may, in one embodiment, be obtained from a data stream, such as acompressed or uncompressed correction data stream. The precise satelliteinformation may be estimated using data from a network of referencestations connected to a processing station for producing a correctiondata stream.

In order to improve the positioning process at the NSS receivers, suchas to improve the performance of position determination systems, someexisting systems involve sending correction information to NSSreceivers. Such correction information may generally be seen ascomprising information useful to correct NSS observations made by areceiver. For example, the correction information may represent datarelating to the NSS system that may be taken into account and used toimprove the estimation of the receiver position. The correctioninformation may comprise correction data relating to NSS satellites,such as, but not limited to, accurate orbital data and accuratesatellite clock data to improve the positioning solution.

The correction information may be computed or prepared by a network ofreference receivers with precisely known positions in a global referenceframe (such as, for example, ITRF2008, which is described for example inZ. Altamimi, X. Collilieux, L. Métivier: ITRF2008: an improved solutionof the international terrestrial reference frame, Journal of geodesy,vol. 85, number 8, page 457-473, 2011). A typically world-wide networkof reference receivers is used for GNSS systems, whereas a regionalnetwork of reference receivers is typically sufficient for RNSS systems.The data from the reference receivers is transmitted for example overthe internet to a processing centre, where the data is collected,synchronized and processed. During the data processing, a variety ofproducts can be generated, including e.g. satellite orbits, satelliteclock errors, GNSS (or RNSS) measurement biases, and atmospheric models.The products (or corrections) are then sent to the rover receivers onthe field. The transmission to the rover may take place in variousdifferent forms, of which the most commonly used are the Internet andsatellite links. For a descriptive example of a global GNSS positioningcorrection service see e.g. WO 2011/034616 A2.

In step s30, ambiguities in the carrier phase of the received rawobservations are estimated, using the precise satellite information orthe information derived therefrom. In other words, using the rawobservations and the precise satellite information (or informationderived therefrom), the ambiguities are estimated for each satellite. Inone embodiment, the ambiguities are set to integer values and thusregarded as resolved. In particular, when the estimated ambiguities aresufficiently close to integer values (e.g., using a threshold), they areset to integer values. In another embodiment, the ambiguities areestimated and set to real number values (float solution). The thresholdcan be any small fractional value, for example one tenth of a cycle,that provides an acceptable improvement in the ambiguity fixingperformance per satellite as shown in FIG. 6, or in the ambiguity fixingper station as shown in FIG. 7.

In one variant, synthesized base station observations (as for exampledescribed in WO 2011/034614 A2, hereinafter referred to as reference[8]) are generated using, i.e. derived from, the precise satelliteinformation, and the synthesized base station observations are then usedto estimate the ambiguities. The synthesized base station observationscontain the modelled satellite orbit, clock, biases information, andoptionally the ionospheric model. Ambiguity resolution is performed withthe single difference observations between the received raw observationsand the synthesized base station. The ambiguity-reduced observations aregenerated after ambiguity fixing, by reconstructing the undifferencedambiguities from the double-difference ambiguities. As a result, in theambiguity-reduced observations, the phase carrier observations arelevelled to a single ambiguity value for every satellite. Ambiguityresolution is, in principle, not mandatory for the described algorithm.Anyway, any kind of optimization correctly exploiting the integer natureof the ambiguities positively affects the estimation of the receivercode biases.

In step s40, combination values are computed based on the received rawobservations together with the estimated ambiguities (in one embodiment,those are resolved integer ambiguities, as explained above), to cancelout the effects of the satellite motion relative to the at least one NSSreceiver (i.e., the effects of what is known in the art as the“geometry”), the effects of the clocks (i.e., the clocks of both thereceiver and the satellite), the effects of the troposphere, and theeffects of the ionosphere. In one embodiment, the computation s40implies that, for each satellite and epoch, the multipath combinationfor L1 and L2 is computed, using code and phase observations afterhaving performed ambiguity estimation (ambiguity-reduced phaseobservations), or, in one embodiment, after having performed ambiguityresolution. For each satellite and epoch, the multipath combination forL1 and L2 is computed, using code and phase synthesized base stationobservations, i.e. from the observables. Then, by subtracting thesynthesized base station observations from the ambiguity-reducedobservations, single-difference multipath combinations are computed (seeequations (19) and (20) below). In particular, (i) the multipathcombination cancels out the effects of the geometry, the ionosphere andthe troposphere delays, (ii) subtracting the synthesized base stationobservations leads to cancelling out the satellite biases and clockerrors using the information provided by the correction stream, and(iii) then, using the ambiguity-reduced observations, the ambiguityparameters are cancelled out.

The multipath combination may constitute the input data to theestimation process. The observation equations are solved through aleast-squares estimation technique for one common parameter (the commonclock) and n (per satellite) biases for each frequency band. Thecorresponding normal equation system has a rank defect of one (becausethe columns of the design matrix are linearly dependent), which isusually solved by imposing a zero mean constraint on the bias estimates.

In step s50, the correction information is generated per satellite,based on the computed combination values. The correction information mayfor example be generated per satellite and frequency (e.g. L1/L2) and/orper satellite and linear combination of frequencies (e.g.ionosphere-free/ionosphere), based on the computed combination values.

The correction information comprises, in one embodiment, the receivercode biases that compromised the ability of GNSS receivers to provideaccurate position information (or at least compromised the ease withwhich GNSS receivers are able to provide accurate position information).The correction information constitutes the output of, or at least aportion of the output of, the calibration process.

The correction information may be generated once and then becomesapplicable to a plurality of receivers of the same or a similar type,i.e., having the same or a similar hardware/firmware, the same or asimilar antenna cable, and the same or a similar antenna. The correctioninformation is used for determining the position, or determining achange in the position, of the NSS receiver(s). In one embodiment, theL1/L2 receiver code biases per satellite, i.e. the correctioninformation, are estimated as well as a common clock parameter for allthe observed satellites. A least-squares estimation method is used witha zero mean constraint over all satellites within a satellite system fora specific frequency band (see equation (21) below). However, variousother methods providing estimates of the satellites biases and theinteger ambiguity may be used for the receiver code bias calibration.

The correction information may for example be in the form of calibrationvalues and/or a calibration table. The correction information may thenbe (a) directly used by the NSS receiver and/or (b) sent to a receiverof the same or similar type and then used by this receiver. Thecalibration values may then be stored in the NSS receiver and subtractedfrom the code observations.

As mentioned above, the prior art approaches are typically suitable forreceiver type specific code biases calibration and require physicalreceiver(s) as reference receiver(s). In order to overcome the need forusing a physical receiver for the calibration, the method of FIG. 1 auses precise satellite information, or information derived therefrom,for example in the form of a data stream provided by a system comprisinga network of reference stations, to define a virtual reference receiver.In such a way, every receiver having access to the precise satelliteinformation, or the information derived therefrom, can be calibratedwithout zero- or short-baseline setup. Various different types, and/orformats, of precise satellite information, or information derivedtherefrom, may be used in the calibration process, such as for exampleas described in U.S. Pat. No. 8,018,377 B2 (hereinafter referred to as“reference [5]”). In such an approach, the global tracking network isused as the reference to calibrate the receiver code bias. In contrastto the zero- and short-baseline techniques, site-specific effects due tothe antenna and/or cable are implicitly accounted for.

The method may be used to better calibrate reference stations (thusallowing improvements to the information and models generated based onobservations obtained at these reference stations) and/or to bettercalibrate rover receivers (leading to a faster convergence and a moreaccurate positioning process).

In one embodiment, receiving s10 raw observations obtained by one of theNSS receiver(s) observing NSS multiple frequency signals from aplurality of NSS satellites occurs over at least one day, as one day isgenerally required to observe all the satellites. This requirement maybe however relaxed for a regional system, and in such a case the zeromean constraint may be modified as well. Namely, it is not needed todefine the zero mean constraint for the whole set of observedsatellites. Defining the zero mean constraint for a subset of theobserved satellite (or just one), is enough to solve the rank defect.

In one embodiment, receiving s10 raw observations obtained by one of theNSS receiver(s) observing NSS multiple frequency signals from aplurality of NSS satellites occurs over a sufficiently long period oftime to be able to observe a given number of satellites.

In one embodiment, when obtaining the precise satellite information,information on: (iv) a precise ionosphere model, is also obtained.

In one embodiment, when obtaining the precise satellite information,information on: (v) a precise troposphere model, is also obtained.

The term “precise” in “precise ionosphere model” and “precisetroposphere model” means, in one embodiment, sufficiently precise toallow a successful ambiguity resolution. For example, the precision ofthe ionosphere and troposphere models may be required to be, as a ruleof thumb, smaller than 0.25 cycles.

In one embodiment, the step of computing s40 combination valuescomprises computing multipath combination values of each frequency. Inthat respect, see for example equations (15) and (16) below.

In one embodiment, step s40 comprises computing ionospheric-free codeminus ionospheric-free phase combination values, i.e. subtracting theionospheric-free phase observations from the ionospheric-free codeobservations. In that respect, see for example equation (22).

In one embodiment, step s40 comprises computing ionospheric code minusionospheric phase combination values, i.e. subtracting the ionosphericphase observations from the ionospheric code observations. In thatrespect, see for example equation (23).

In one embodiment, step s40 comprises computing Melbourne-Wöbbena (MW)combination values. In that respect, see for example equation (26).

In one embodiment, step s40 comprises computing ionospheric-free codeminus ionospheric-free phase combination values, and ionospheric codeminus ionospheric phase combination values. In that respect, see forexample equations (22) and (23).

In one embodiment, step s40 comprises computing ionosphere-free codeminus ionosphere-free phase combination values, and MW combinationvalues. In that respect, see for example equations (22) and (26).

In one embodiment, step s40 comprises computing ionospheric code minusionospheric phase combination values and MW combination values. In thatrespect, see for example equations (23) and (26).

Such combinations (corresponding, for example, to (i) equations (22) and(23), (ii) equations (22) and (26), and (iii) equations (23) and (26))are similar to the multipath combination, as it is possible to find alinear transformation between the two sets of combinations (see forexample equation (27)). Further, see for example equations (28) to (32)regarding the estimation of the receiver code biases.

In one embodiment, the raw observations include observations for bothGPS and GLONASS satellites. In general however, the calibration methodaccording to embodiments of the invention may be applied to anyconstellation of GNSS satellites. The method is independent of theconsidered constellation. The method is all the more beneficial as theaddressed receiver code biases are bigger, such for example for someGLONASS receivers.

FIG. 1 b is a flowchart of a method in one embodiment of the invention,showing a more specific embodiment than the one described with referenceto FIG. 1 a in that, in step s30, the ambiguities are set to integervalues and thus regarded as resolved. The resolved ambiguities are thenused in step s40 for computing the combination values. Theconsiderations discussed with reference to FIG. 1 a otherwise also applyto FIG. 1 b.

FIG. 1 c is a flowchart of a method in one embodiment of the invention,showing a more specific embodiment than the one described with referenceto FIG. 1 b. Namely, in step s25, the precise satellite information isused to generate, i.e. to derive, synthetized base station observations,which are then used in step s30 to resolve the ambiguities. In step s35,the resolved ambiguities and the received raw observations are used togenerate ambiguity reduced observations. The ambiguity reducedobservations are phase observations from which the estimated (optimized)ambiguities are subtracted. These ambiguity reduced observations havethe property that any double differenced ambiguity computed from them iszero. Then, combination values are computed s40 based on the singledifference between the generate ambiguity reduced observations and thesynthetized based stations observations. The correction information,such as, in one embodiment, the receiver code bias information persatellite, is then generated s50 based on the computed combinationvalues. The considerations discussed with reference to FIGS. 1 a and 1 botherwise apply to FIG. 1 c as well.

Let us now further explain the context in which some embodiments of theinvention have been developed, for a better understanding thereof. Inparticular, the zero- and short-baseline calibrations are described inmore detail (section A). Then, further embodiments of the invention arealso described and discussed (sections B to F), and the performancethereof is discussed (section D).

A. Zero- and Short-Baseline Calibration

Zero- and short-baseline calibration requires only code (pseudorange)observations. The code observation between satellite s and receiver rfor frequency k (i.e. GPS L1, L2), modulation type m (i.e. GPS L2C,L2P/Y) is modeled as:

P _(r,k) ^(s)=ρ_(r) s+cΔt _(r) −cΔt ^(s) +T _(r) ^(s) −I _(r,k) ^(s) +B_(r,k) ^(s) −B _(k) ^(s)+υ_(r,k) ^(s)  (1)

where:

ρ_(r) ^(s)is the geometric range of satellite s at signal transmissiontime and receiver r at signal reception time;

c is the speed of light, cΔt_(r) is the receiver clock error, cΔt^(s) isthe satellite clock error;

T_(r) ^(s) is the tropospheric delay for satellite s, wherein thetropospheric effect is frequency/modulation type independent;

I_(r,k) ^(s) is the ionospheric delay for satellite s at frequency k.The ionospheric effect is frequency dependent. For given two frequenciesk1 and k2,

${I_{r,{k\; 1}}^{S} = {\frac{\lambda_{k\; 1}^{2}}{\lambda_{k\; 2}^{2}}I_{r,{k\; 2}}^{S}}},$

where λ_(k1), λ_(k1) are the wavelength for frequency k1 and k2respectively;

B_(k) ^(s) is the satellite code bias for frequency k which is caused bysatellite hardware delay;

B_(r,k) ^(s) is the receiver code bias per satellite for frequency k.This bias is caused by receiver hardware delay when tracking differentsatellite signals;

υ_(r,k) ^(s) represents the code noise and multipath.

Modern receivers can track more than one signal (modulation) perfrequency, e.g. GPS L1 CA, L1 P/Y for GPS L1 frequency, GPS L2C andL2P/Y for L2 frequency. The modulation type is ignored for simplicity inequation (1) and the following description, which is applicable for anysuitable modulation type.

Zero- and short-baseline calibration uses single difference codeobservations between two receivers. By single differencing, thesatellite clock error is cancelled out. For a zero-baseline setup, thetroposphere and ionosphere effects are cancelled out totally. For ashort-baseline setup which is few meters apart, the residual troposphereand ionosphere effect can be ignored. The single difference codeobservation between receiver r1 and r2 is modeled as:

P _(r1r2,k) ^(s)=ρ_(r1r2) ^(s) +cΔt _(r1,r2) B _(r1r2,k) ^(s)+υ_(r1r2,k)^(s)  (2)

where:

ρ_(r1r2) ^(s) is the single difference geometric range, which can becalculated with satellite ephemeris and position of receivers r1 and r2(for zero-baseline calibration this term is zero);

cΔt_(r1,r2) is the single difference receiver clock error;

B_(r1,r2,k) ^(s) is the code bias per satellite between two receivers;and

υ_(r1r2,k) ^(s) is the single difference code noise and multipath.

With all observed satellites and multiple epochs of data (preferablymore than one day), B_(r1r2,k) ^(s) can be estimated with aleast-squares adjustment for one common parameter (the common receiverclock) and n code biases per satellite for each frequency band. Thecorresponding normal equation system has a rank defect of one which isusually solved by imposing a zero mean condition on the bias estimation(for details, see section “C. Design matrix and zero mean condition”)for each signal (e.g., GPS L1CA, L2P/Y, L2C, GLONASS L1CA, L2CA, etc.).

B. Code Bias Calibration with Precise Satellite Orbit/Clock/BiasInformation

Both zero- and short-baseline calibration require at least one referencereceiver, i.e. dedicated equipment locally arranged near the receiver tobe calibrated. The calibrated code bias is relative to the referencereceiver(s).

With the precise satellite orbit and clock information (or informationderived therefrom) in accordance with one embodiment of the invention,it is possible to calibrate the receiver code biases per satellitewithout a reference receiver. In other words, the receiver is calibratedagainst the reference station network which is used to generate theprecise satellite orbit and clock information.

Reference [3] describes how to estimate the code biases inionosphere-free linear combination in precise point positioning (PPP)data processing. Unfortunately, this method cannot estimate code biasesfor each individual signal. If the troposphere and ionosphere delay canbe obtained or estimated, the code biases for each signal can beobtained by equation (1). The accuracy of the estimated code biasesdepends on the accuracy of orbit and clock, in particular the accuracyof troposphere and ionosphere delay.

Some advanced PPP services provide satellite biases information inaddition to precise orbit and clock, which enables the carrier phaseambiguity resolution on the user receiver (see Ge, M, G. Gendt, M.Rothacher, C. Shi, J. Liu, Resolution of GPS carrier phase ambiguitiesin precise point positioning (PPP) with daily observations, Journal ofGeodesy, 2008, hereinafter referred to as reference [6], and Leandro,R., H. Landau, M. Nitschke, M. Glocker, S. Seeger, X. Chen, A, Deking,M. Ben Tahar, F.

Zhang, R. Stolz, N. Talbot, G. Lu, K. Ferguson, M. Brandi, V. GomezPantoja, A. Kipka (2011) “RTX Positioning: the Next Generation ofcm-accurate Real-time GNSS Positioning”, Paper presented atION-GNSS-2011, Sep. 20-23, 2011, Portland, Oreg., USA, hereinafterreferred to as reference [7]). The position accuracy of the userreceiver can achieve centimeter level accuracy. This enables performingprecise receiver code bias calibration without the need of precisetroposphere and ionosphere information. The approach uses both code andcarrier phase observations and requires ambiguity resolution on the userreceiver.

The carrier phase observation can be modeled as:

L _(r,k) ^(s)=ρ_(r) ^(s) +cΔt _(r) −cΔt ^(s) +T _(r) ^(s) +I _(r,k) ^(s)+b _(r,k) −b _(,k) ^(s)+λ_(k) N _(r,k) ^(s)+ε_(r,k) ^(s)  (3)

where:

cΔt_(r),cΔt^(s) are the receiver and satellite clock error;

b_(r,k), b_(,k) ^(s) are the receiver and satellite phase biasesrespectively;

λ_(k) is the wavelength of carrier phase;

N_(r,k) ^(s) is the integer ambiguity; and

ε_(r,k) ^(s) is the carrier phase observation noise including multipath.

We see that the clock errors are separated from the satellite phasebiases. This holds also for the ionosphere free combination of the phaseobservations: the ionosphere free receiver and satellite clock errorsare separated from the ionosphere free combination of the receiver andsatellite biases. Another definition of the clock error can be used,which lumps together the receiver and satellites clocks and the biases.The ionosphere free combination of such re-defined clock errors iscalled phase-leveled clock error. Phase leveled clock error is explainedin Part 9 of reference [8]. The phase leveled clock error is computedwith ionospheric-free phase observations from a global network andenables the ambiguity fixing with user receiver only. Ionospheric-freephase observations can be built if phase observations are available fromat least two frequencies. For example, the L1, L2 ionospheric-free phaseobservation can be written as:

$\begin{matrix}{L_{{IF}_{r}}^{s} = {{{\frac{\lambda_{2}^{2}}{\lambda_{2}^{2} - \lambda_{1}^{2}}L_{r,1}^{s}} - {\frac{\lambda_{1}^{2}}{\lambda_{2}^{2} - \lambda_{1}^{2}}L_{r,2}^{s}}} = {\rho_{r}^{s} + {c\; \delta \; t_{r}} - {c\; \delta \; t^{s}} + T_{r}^{s} + N_{C_{r}}^{s} + ɛ_{C}}}} & (4)\end{matrix}$

where the ionosphere free combination of the receiver and satellitephase biases are lumped up into the phase leveled clock error,

$\begin{matrix}{{c\; \delta \; t_{r}} = {{{c\; \Delta \; t_{r}} + {b_{r,C}\mspace{14mu} {and}\mspace{14mu} c\; \delta \; t^{2}}} = {{c\; \Delta \; t^{s}} + b_{,C}^{s}}}} & (5) \\{{b_{r,C} = {{\frac{\lambda_{2}^{2}}{\lambda_{2}^{2} - \lambda_{1}^{2}}b_{r,1}} - {\frac{\lambda_{1}^{2}}{\lambda_{2}^{2} - \lambda_{1}^{2}}b_{r,2}\mspace{14mu} {and}}}}{b_{,C}^{s} = {{\frac{\lambda_{2}^{2}}{\lambda_{2}^{2} - \lambda_{1}^{2}}b_{,1}^{s}} - {\frac{\lambda_{1}^{2}}{\lambda_{2}^{2} - \lambda_{1}^{2}}b_{,2}^{s}}}}} & (6) \\{N_{C_{r}}^{s} = {{\frac{\lambda_{1}\lambda_{2}^{2}}{\lambda_{2}^{2} - \lambda_{1\;}^{2}}N_{r,1}^{s}} - {\frac{\lambda_{1}^{2}\lambda_{2}}{\lambda_{2}^{2} - \lambda_{1}^{2}}N_{r,2}^{s}}}} & (7)\end{matrix}$

λ₁,λ₂ are the wavelength for L1 and L2, respectively, and N_(r,1) ^(s),N_(r,2) ^(s) are the integer ambiguity for L1 and L2, respectively.ε_(C) is the carrier phase noise in ionospheric free phase combination.The ionosphere free ambiguity is expressed in linear units.

The phase leveled clock error is not unique. Depending on how theambiguity is resolved and leveled, phase leveled clock error can beshifted by a combination of integer number of N1 and N2 ambiguitydefined by equation (7). The effect is common to all satellites in thesame satellite system and thus absorbed by the receiver clock term.

And the L1/L2 ionospheric phase combination (mapped to frequency L1) canbe written as:

$\begin{matrix}{{L_{I_{r,1}^{s}} = {{{- \frac{\lambda_{1}^{2}}{\lambda_{2}^{2} - \lambda_{1}^{2}}}( {L_{r,1}^{s} - L_{r,2}^{s}} )} = {I_{r,1}^{s} + b_{r,I} - b_{,I}^{s} + N_{I_{r}^{s}} + ɛ_{I}}}}{{where}\text{:}}} & (8) \\{b_{r,I} = {{\frac{\lambda_{1}^{2}}{\lambda_{2}^{2} - \lambda_{1}^{2}}( {b_{r,2} - b_{r,1}} )\mspace{14mu} {and}\mspace{14mu} b_{,I}^{s}} = {\frac{\lambda_{1}^{2}}{{\lambda_{2}^{2} - \lambda_{1}^{2}}\;}( {b_{2}^{s} - b_{1}^{s}} )}}} & (9) \\{N_{I_{r}^{s}} = {{{- \frac{\lambda_{1}^{3}}{\lambda_{2}^{2} - \lambda_{1}^{2}}}N_{r,1}^{s}} + {\frac{\lambda_{1}^{2}\lambda_{2}}{\lambda_{2}^{2} - \lambda_{1}^{2}}N_{r,2}^{s}}}} & (10)\end{matrix}$

b_(r,I) and b_(,I) ^(s) are the ionospheric phase bias for receiver andsatellite, respectively. ε_(I) is the carrier phase noise in ionosphericphase combination.

In PPP server process, the satellite clock error is estimated based onionospheric-free code observations, so that the estimated satelliteclock error is so-called code leveled clock (Part 6 of reference [8])(this satellite clock error is estimated through the ionosphere-freecode combination, hence it also contains the ionosphere-free combinationof the satellite code biases). The code leveled clock is defined as thesatellite clock error plus the ionospheric-free satellite code bias(this clock error is the sum of two parts which have different behaviourin time: the clock part is rapidly changing whereas the second is almostconstant in time):

$\begin{matrix}{{cdt}^{s} = {{c\; \Delta \; t^{s}} + {\frac{\lambda_{2}^{2}}{\lambda_{2}^{2} - \lambda_{1}^{2}}B_{,1}^{s}} - {\frac{\lambda_{1}^{2}}{\lambda_{2}^{2} - \lambda_{1}^{2}}B_{,2}^{s}}}} & (11)\end{matrix}$

Another satellite bias is the satellite Differential Code Bias (DCB),which is the difference of code bias between two signals. The L2-L1satellite DCB is defined as:

B _(I) ^(s) =B _(,2) ^(s) −B _(,1) ^(s)  (12)

From equations (11) and (12), the following relationships can bederived:

$\begin{matrix}{{{{c\; \Delta \; t^{s}} + B_{,1}^{s}} = {{cdt}^{s} + {\frac{\lambda_{1}^{2}}{\lambda_{2}^{2} - \lambda_{1}^{2}}B_{I}^{s}}}}{and}} & (13) \\{{{c\; \Delta \; t^{s}} + B_{,2}^{s}} = {{cdt}^{s} + {\frac{\lambda_{2}^{2}}{\lambda_{2}^{2} - \lambda_{1}^{2}}B_{I}^{s}}}} & (14)\end{matrix}$

With equations (1), (4), and (8), a special code phase combination canbe built, which is geometry-free and ionosphere-free. This combinationis the so-called multipath combination, it is also called the divergencefree combination. Further considering equations (11) and (12), L1 and L2multipath combination can be written as:

$\begin{matrix}\begin{matrix}{{m\; p_{r,1}^{s}} = {P_{r,1}^{s} - L_{{IF}_{r}^{s}} + L_{I_{r,1}^{s}}}} \\{= {( {{c\; \delta \; t^{s}} - {cdt}^{s}} ) - ( {{\frac{\lambda_{1}^{2}}{\lambda_{2}^{2} - \lambda_{1}^{2}}B_{I}^{s}} + b_{I}^{s}} ) - ( {N_{c_{r}^{s}} - N_{I_{r}^{s}}} ) +}} \\{{( {{c\; \Delta \; t_{r}} - {c\; \delta \; t_{r}} + b_{r,I}} ) + B_{r,1}^{s} + ɛ_{m\; p\; 1}}}\end{matrix} & (15) \\\begin{matrix}{{m\; p_{r,2}^{s}} = {P_{r,2}^{s\;} - L_{{IF}_{r}^{s}} + {\frac{\lambda_{2}^{2}}{\lambda_{1}^{2}}L_{I_{r,1}^{s}}}}} \\{= {( {{c\; \delta \; t^{s}} - {cdt}^{s}} ) - ( {{\frac{\lambda_{2}^{2}}{\lambda_{2}^{2} - \lambda_{1}^{2}}B_{I}^{s}} + {\frac{\lambda_{2}^{2}}{\lambda_{1}^{2}}b_{I}^{s}}} ) -}} \\{{( {N_{c_{r}^{s}} - {\frac{\lambda_{2}^{2}}{\lambda_{1}^{2}}N_{I_{r}^{s}}}} ) + ( {{c\; \Delta \; t_{r}} - {c\; \delta \; t_{r\;}} - {{+ \frac{\lambda_{2}^{2}}{\lambda_{1}^{2}}}b_{r,I}}} ) +}} \\{{B_{r,2}^{s} + ɛ_{m\; p\; 2}}}\end{matrix} & (16)\end{matrix}$

In equations (15) and (16), the first pair of brackets contains thedifference of phase leveled and code leveled satellite clock error; thesecond pair of brackets contains the satellite DCB and satelliteionospheric phase bias term; the third pair of brackets contains theionospheric-free and ionospheric ambiguity term; and the fourth pair ofbrackets contains the receiver clock error and ionospheric receiverphase bias term, this term being the same for all satellites within onesatellite system, so that it can be eliminated epoch by epoch in aleast-squares adjustment. ε_(mp1) and ε_(mp2) are the noise in L1 and L2multipath combination.

Assuming that a PPP service provides the difference between code leveledand phase leveled satellite clock error, satellite DCB and ionosphericphase bias, and the ambiguities of the user receiver can be resolvedwith the PPP server correction data, the receiver code bias persatellite for L1 and L2 can be estimated by using multiple epochs datawith the method described in section “C. Design matrix and zero meancondition”.

Moreover, according to equation (18) of US2013/0044026 A1 (hereinafterreferred to as reference [9]), satellite MW bias can be used to replacesatellite DCB if the PPP service provides the difference between codeand phase clock, and it also provides the ionospheric phase bias (thisis because there is a linear relationship between the DCB and the MWphase biases).

Another variant is to generate synthetic reference data with the PPPserver correction data as described in reference [9]. Further forming L1and L2 multipath combination as following:

$\begin{matrix}{{m\; p_{{GVRS}_{r,1}^{s}}} = {( {{c\; \delta \; t^{s}} - {cdt}^{s}} ) - ( {{\frac{\lambda_{1}^{2}}{\lambda_{2}^{2} - \lambda_{1}^{2}}B_{I}^{s}} + b_{I}^{s}} )}} & (17) \\{{m\; p_{{GVRS}_{r,2}^{s}}} = {( {{c\; \delta \; t^{s}} - {cdt}^{s}} ) - ( {{\frac{\lambda_{2}^{2}}{\lambda_{2}^{2} - \lambda_{1}^{2}}B_{I}^{s}} + {\frac{\lambda_{2}^{2}}{\lambda_{1}^{2}}b_{I}^{s}}} )}} & (18)\end{matrix}$

Differencing between the multipath combination of user receiver andsynthetic reference data,

$\begin{matrix}{{{m\; p_{r,1}^{s}} - {m\; p_{{GVRS}_{r,1}^{s}}}} = {{- ( {N_{c_{r}^{s}} - N_{I_{r}^{s}}} )} + ( {{c\; \Delta \; t_{r}} - {c\; \delta \; t_{r}} + b_{r,I}} ) + B_{r,1}^{s} + ɛ_{m\; p\; 1}}} & (19) \\{{{m\; p_{r,2}^{s}} - {m\; p_{{GVRS}_{r,2}^{s}}}} = {{- ( {N_{c_{r}^{s}} - {\frac{\lambda_{2}^{2}}{\lambda_{1}^{2}}N_{I_{r}^{s}}}} )} + ( {{c\; \Delta \; t_{r}} - {c\; \delta \; t_{r}} + {\frac{\lambda_{2}^{2}}{\lambda_{1}^{2}}b_{r,I}}} ) + B_{r,2}^{s} + ɛ_{m\; p\; 2}}} & (20)\end{matrix}$

With the integer ambiguity of the user receiver resolved, the receivercode bias per satellite for L1 and L2 can be estimated.

The above-described method uses multipath combination to estimate thecode biases per satellite for each signal directly. It is also possibleto estimate the code biases for combinations of code observations, i.e.ionospheric free code bias, ionospheric code bias, narrowlane bias, etc.

The ionospheric-free code observation of L1 and L2 code can be writtenas:

$\begin{matrix}{P_{{IF}_{r}^{s}} = {{{\frac{\lambda_{2}^{2}}{\lambda_{2}^{2} - \lambda_{1}^{2}}P_{r,1}^{s}} - {\frac{\lambda_{1}^{2}}{\lambda_{2}^{2} - \lambda_{1}^{2}}P_{r,2}^{s}}} = {\rho_{r}^{s} + {c\; \Delta \; t_{r}} - {cdt}^{s} + T_{r}^{s} + B_{r,C}^{s} + v_{r,C}^{s}}}} & (21)\end{matrix}$

By subtracting equation (4) from equation (21), we get:

P _(IF) _(r) ^(s) −L _(1F) _(r) ^(s)=(cδt ^(s) −cdt ^(s))−N _(C) _(r)^(s)+(cΔt _(r) −cδt _(r))+B _(r,C) ^(s)+ν_(r,C) ^(s)−ε_(r,C) ^(s)  (22)

With estimated ionospheric-free ambiguity and the satellite code andphase leveled clock obtained from a PPP service, the ionospheric-freecode bias per satellite can be estimated. This bias is useful to reducethe positioning error when the NSS receiver uses ionospheric free codeand phase observations to calculate the position.

The receiver ionospheric code bias per satellite can be derived insimilar way. The ionospheric code observation of L1 and L2 code is usedby subtracting the ionospheric phase observation from the ionosphericcode observation:

$\begin{matrix}{{\underset{\underset{= {P_{r,2}^{s} - P_{r,1}^{s}}}{}}{P_{I_{r}^{s}}} - {\frac{\lambda_{2}^{2} - \lambda_{1}^{2}}{\lambda_{1}^{2}}L_{I_{r,1}^{s}}}} = {B_{r,I}^{s} - ( {B_{I}^{s} - {\frac{\lambda_{2}^{2} - \lambda_{1}^{2}}{\lambda_{1}^{2}}b_{I}^{s}}} ) - {\frac{\lambda_{2}^{2} - \lambda_{1}^{2}}{\lambda_{1}^{2}}b_{r,I}} - {\frac{\lambda_{2}^{2} - \lambda_{1}^{2}}{\lambda_{1}^{2}}N_{r,I}^{s}} + ( {v_{r,I}^{s} - {\frac{\lambda_{2}^{2} - \lambda_{1}^{2}}{\lambda_{1}^{2}}ɛ_{I}}} )}} & (23)\end{matrix}$

With estimated ionospheric ambiguity, the satellite DCB and ionosphericphase bias obtained from a PPP service, the receiver ionospheric codebias per satellite can be estimated.

Furthermore, the narrowlane code bias can be derived from the narrowlanecode observations minus widelane phase observations (Melbourne-Wübbena(MW) combination). The narrowlane code for L1/L2 frequency is:

$\begin{matrix}{P_{{NL}_{r}^{s}} = {{\frac{\lambda_{1}\lambda_{2}}{\lambda_{1} + \lambda_{2}}( {\frac{P_{r,1}^{s}}{\lambda_{1}} + \frac{P_{r,2}^{s}}{\lambda_{2}}} )} = {\rho_{r}^{s} + {c\; \Delta \; t_{r}} - {c\; \Delta \; t^{s}} + T_{r}^{s} - {\lambda_{1}I_{r,1}^{s}} + B_{r,{NL}}^{s} - B_{NL}^{s} + v_{{NL}_{r}^{s}}}}} & (24)\end{matrix}$

where B_(r,NL) ^(s) and B_(NL) ^(s) are the narrow-lane combinations ofthe receiver code bias per satellite and the satellite code bias,respectively. ν_(NL) _(r) ^(s) is the code noise in narrowlane codecombination. And widelane phase is:

$\begin{matrix}{L_{{WL}_{r}^{s}} = {{\frac{\lambda_{1}\lambda_{2}}{\lambda_{1} + \lambda_{2}}( {\frac{L_{r,1}^{s}}{\lambda_{1}} - \frac{L_{r,2}^{s}}{\lambda_{2}}} )} = {\rho_{r}^{s} + {c\; \Delta \; t_{r}} - {c\; \Delta \; t^{s}} + T_{r}^{s} - {\lambda_{1}I_{r,1}^{s}} + \; b_{{WL}_{r}} - b_{WL}^{s} + {\frac{\lambda_{1}\lambda_{2}}{\lambda_{1} + \lambda_{2}}( {N_{r,1}^{s} - N_{r,2}^{s}} )} + ɛ_{{WL}_{T}^{s}}}}} & (25)\end{matrix}$

where b_(WL) _(r) and b_(WL) ^(s) are the wide-lane combinations of thereceiver and satellite phase bias, respectively. ε_(WL) _(r) ^(s) is thecarrier phase noise in widelane phase combination.

By subtracting the wide-lane phase from the narrow-lane code, we get:

$\begin{matrix}{{P_{{NL}_{r}^{s}} - L_{{WL}_{r}^{s}}} = {B_{r,{NL}}^{s} - b_{{WL}_{r}} - \underset{\underset{= B_{M\; W}^{2}}{}}{( {B_{NL}^{s} - b_{WL}^{s}} )} - {\frac{\lambda_{1}\lambda_{2}}{\lambda_{1} + \lambda_{2}}\underset{\underset{= N_{{WL}_{r}^{s}}}{}}{( {N_{r,1}^{s} - N_{r,2}^{s}} )}} + v_{{NL}_{r}^{s}} - ɛ_{{WL}_{r}^{s}}}} & (26)\end{matrix}$

In equation (26), the term in the first pair of brackets on theright-hand side of the equation represents the satelliteMelbourne-Wübbena (MW) bias, see Part 7 of reference [8]. By using theestimated widelane ambiguity N_(WL) _(r) ^(s), satellite MW bias B_(MW)^(s) from a PPP service and, assuming that the receiver widelane phasebias b_(WL) _(r) has the same value for all satellites in a givensatellite system (i.e. in a given satellite constellation, such as forexample in the GPS or in the GLONASS satellite system) for each epoch,the receiver narrowlane code bias per satellite can be estimated. Thisnarrowlane code bias is useful to solve the widelane ambiguity for a NSSreceiver and/or is helpful to resolve the ionospheric-free ambiguity.

With the estimated code bias combination (equations (22), (23) and(26)), the code bias of each signal can be derived with two code biascombination via a linear relationship. The linear relationships of thebiases are:

$\begin{matrix}\{ {\begin{matrix}{B_{r,C}^{s} = {{\frac{\lambda_{2}^{2}}{\lambda_{2}^{2} - \lambda_{1}^{2}}B_{r,1}^{s}} - {\frac{\lambda_{1}^{2}}{\lambda_{2}^{2} - \lambda_{1}^{2}}B_{r,2}^{s}}}} \\{B_{r,I}^{s} = {B_{r,1}^{s} - B_{r,2}^{s}}} \\{B_{r,{NL}}^{s} = {{\frac{\lambda_{2}}{\lambda_{1} + \lambda_{2}}B_{r,1}^{s}} + {\frac{\lambda_{1}}{\lambda_{1} + \lambda_{2}}B_{r,2}^{s}}}}\end{matrix}\quad}  & (27)\end{matrix}$

The code bias combinations that may be used for such purpose are, inthree embodiments respectively:

-   -   1) Ionosphere free and ionosphere code bias. In that respect,        see for example equations (22) and (23).    -   2) Ionosphere free and narrow lane code bias. In that respect,        see for example equations (22) and (26).    -   3) Narrow lane and ionosphere code bias. In that respect, see        for example equations (23) and (26).

C. Design Matrix and Zero Mean Condition

From the previous sections, it can be noted that the observationequations related to different frequencies are decoupled. Hence, it ispossible to resolve each of the associated least squares problemsseparately. For each of them, the design matrix has the following form:

$\begin{matrix}{A = \begin{bmatrix}I_{n} & e_{n} & \; & \; \\\vdots & \; & \ddots & \; \\I_{n} & \; & \; & e_{n}\end{bmatrix}} & (28)\end{matrix}$

where I_(n) is the identity matrix, n is the number of satellitesobserved and e_(n) is a n-by-1 column matrix the entries of which arel's. The matrix A has a rank defect of 1. In order to invert the matrixA, an additional constraint equation must be added. The constraintequation reads as:

C=[e _(n) ^(T)0_(1,k)]=0.  (29)

where 0_(1,k) is a 1-by-k row matrix of 0's, k is the number of epochs.The choice of the constraint equation may be different (for example, itis possible to just fix the bias value of one satellite to a givenvalue, or the common clock at an arbitrary epoch.) The constraineddesign matrix A_(C) is then:

$\begin{matrix}{A_{C} = {\begin{bmatrix}A \\C\end{bmatrix}.}} & (30)\end{matrix}$

The normal equations read as:

x=(A _(C) ^(T) WA _(C))⁻¹ A _(C) ^(T) Wy  (31)

where x are the estimates of the receiver code biases per satellite, yis the set of observations for the considered frequency, as defined byequations (15) and (16), or equations (19) and (20), or equations (22),(23) and (26) and W is the weight matrix. Such a matrix is diagonal andits elements are defined as:

$\begin{matrix}{W_{i} = \lbrack \frac{\sin \; \theta_{i}}{\sigma_{i}} \rbrack^{2}} & (32)\end{matrix}$

where θ_(i) is the elevation of the i-th satellite and σ_(i) is the codenoise at zenith.

D. Performance

The methods and apparatus of the invention involve the generation ofcorrection information, and, in some embodiments, more particularly thegeneration of receiver code biases per satellite. The performance ofsome of these embodiments of the invention is discussed in the presentsection.

FIG. 2 illustrates the effects of the receiver code biases per satelliteon the double-difference residuals of the multipath combination(GLONASS, L1CA; BEDF station, Nov. 15, 2013), after ambiguity fixing(the BEDF station belongs to a Trimble global network and is located incentral U.S. (latitude +40 deg, longitude −95 deg)). The data used hasbeen collected at station BEDF on Nov. 15, 2013. In the figure, X axisrepresents the GPS time of week in seconds, and Y axis represents thecode biases in meter. The double-difference multipath residuals havebeen computed using GLONASS R22 as reference satellite, and satellitesR03 and R13. FIG. 2 thus shows a typical example of code biases ofGLONASS satellites R03 and R13 relative to the reference satellite R22on L1CA signal. The mean value of the multipath combination for thedouble difference R22-R03 is represented by the solid line, while thesame quantity for the double difference R22-R13 is represented by thedashed line. The difference between the mean values points out thepresence of a differential receiver code bias between satellite R03 andsatellite R13 that reaches 80 cm, A bias of this size always impairsambiguity resolution.

FIG. 3 shows the receiver code biases for the same satellites as FIG. 2,after having applied the correction information generated in a methodaccording one embodiment of the invention. Compared to FIG. 2, now thebias between the mean values of the double difference multipath R22-R03and R22-R13 is less than 5 cm. This value is low enough not to affectthe performance of the ambiguity resolution. FIGS. 2 and 3 thereforeshow that, after applying the bias corrections, the residuals areunbiased.

In some embodiments of the invention, correction values are generatedwhich have a similar accuracy as that of the correction values providedby methods requiring dedicated hardware, such for example theabove-described zero-baseline calibration. This is illustrated by FIGS.4 and 5 for the GPS and the GLONASS system, respectively.

In FIG. 4, the difference between the receiver code biases values (GPSL1CA/L2PE) estimated for each receiver using a method according to anembodiment of the invention (white bars) is compared to the receivercode bias values estimated using a zero-baseline approach (black bars).The zero-baseline experiment took place in Höhenkirchen, Germany, on dayof year (doy) 03, 2014. FIG. 5 shows the same comparison for GLONASSL1CA/L2CA. FIGS. 4 and 5 show that the accuracy of the correction valuesestimated using a method in one embodiment of the invention are similarto the accuracy of the correction values estimated using thezero-baseline experiment, at the level of 1-2 centimetres at most.

In some embodiments of the invention, the performance of ambiguityresolution is improved. To illustrate the improvement, the percentage offixed ambiguities per satellite is shown in FIG. 6. The black barsrepresent the performance for an uncalibrated receiver, while the greybars show the performance for the same receiver after having applied thecorrections estimated in accordance with an embodiment of the invention.This calibration increases the percentage of the fixed GLONASSambiguities to a level comparable to GPS. In particular, the value isnow higher than 90 percent for all the GLONASS satellites. Animprovement of a few percent is often enough to drastically shorten thetime needed for precise positioning. The dataset was collected by BEDFstation (day of year 319, 2013). Satellites G27, G30, R02 and R08 werenot present in the considered dataset. Zero value means thecorresponding value is not present in the dataset.

In addition, in some embodiments of the invention, the performance ofthe ambiguity resolution, as indicated by the “ambiguity fixing rate”(as a percentage) performance metric, is improved for a network ofworld-wide distributed reference stations (in accordance, for example,with US 2012/0163419 A1). The improvement is measured by the differencesin the ambiguity fixing rate per station, between the calibrated anduncalibrated cases, as shown in FIG. 7. The improvement due to receivercode bias calibration is represented by positive values. Negative valuescorrespond to the stations for which the biases are not corrected(indicated by brackets on the x-axis). The dataset was collected on Nov.10-12, 2013. In other words, FIG. 7 shows the difference between thefixing rate obtained by the MW processor after receiver code biascalibration, and before, for the same dataset. The stations showing aworsening, corresponding to a decrease of the fixing ratio, are thosefor which the biases have not been corrected.

As apparent from what precedes, embodiments of the invention providecalibration values for the receiver code biases per satellite, thequality of which is comparable to the methods using zero-base linecalibration, but without requiring a dedicated hardware or physicalconstraint on the baseline length. The methods may be employed for thecalibration of a single receiver as well as the calibration of a networkof receivers. Therefore, some embodiments of the invention are wellsuited for the remote calibration of a large number of worldwidedistributed receivers. The method not only estimates the receiver codebias, but also takes into account the inherent bias due to the antennaand cable. Finally, the ambiguity fixing rate is also improved both fora single receiver and a network of receivers.

E. Apparatus

In one embodiment, schematically illustrated by FIG. 10, an apparatus100 is provided for generating correction information associated with atleast one NSS receiver. The correction information comprises informationfor correcting pseudorange observations and, as mentioned above, thepseudorange observations useful for determining a position of the atleast one NSS receiver. The apparatus 100 comprises fives units.

The raw observations receiving unit 10 is configured for receiving rawobservations obtained by one of the at least one NSS receiver observingNSS multiple frequency signals from a plurality of NSS satellites overmultiple epochs.

The precise satellite information obtaining unit 20 is configured forobtaining information, hereinafter referred to as “precise satelliteinformation”, on: (i) the orbit position of each one of the plurality ofNSS satellites, (ii) a clock offset of each one of the plurality of NSSsatellites, and (iii) a set of biases associated with each one of theplurality of NSS satellites, or is configured for obtaining informationderived from the precise satellite information.

The ambiguities estimating unit 30 is configured for estimatingambiguities in the carrier phase of the received raw observations, usingthe precise satellite information or the information derived therefrom.In one embodiment, as explained above, the ambiguities are set tointeger values, and thus regarded as resolved. In one embodiment, asdiscussed with reference to FIG. 1 c, synthetized base stationobservations are generated based on, i.e. derived from, the precisesatellite information, and the synthetized base station observations arethen used in the ambiguities estimating unit 30 to estimate theambiguities, or, in one embodiment, to resolve the ambiguities tointeger values.

The combination values computing unit 40 is configured for computingcombination values based on the received raw observations together withthe estimated ambiguities, to cancel out the effects of the satellitemotion relative to the at least one NSS receiver (i.e. the effects ofthe geometry), the effects of the clocks, the effects of the troposphereand the effects of the ionosphere.

The correction information generating unit 50 is configured forgenerating the correction information per satellite and frequency, basedon the computed combination values.

In one embodiment, the raw observations receiving unit 10 is configuredfor receiving raw observations obtained by one of the at least one NSSreceiver observing NSS multiple frequency signals from a plurality ofNSS satellites over at least one day.

In one embodiment, the precise satellite information obtaining unit 20is further configured for obtaining information on: (iv) a preciseionosphere model.

In one embodiment, the precise satellite information obtaining unit 20is further configured for obtaining information on: (v) a precisetroposphere model.

In one embodiment, the combination values computing unit 40 isconfigured for computing multipath combination values of each frequency.In that respect, see for example equations (15) and (16) above.

In one embodiment, the combination values computing unit 40 isconfigured for computing the ionospheric-free code minusionospheric-free phase combination values. In that respect, see forexample equation (22).

In one embodiment, the combination values computing unit 40 isconfigured for computing the ionospheric code minus ionospheric phasecombination values. In that respect, see for example equation (23).

In one embodiment, the combination values computing unit 40 isconfigured for computing Melbourne-Wübbena (MW) combination values. Inthat respect, see for example equation (26).

In one embodiment, the combination values computing unit 40 isconfigured for computing the ionospheric free code minus ionosphericfree phase combination values, and the ionospheric code minusionospheric phase combination values. In that respect, see for exampleequations (22) and (23).

In one embodiment, the combination values computing unit 40 isconfigured for computing the ionospheric free code minus ionosphericfree phase combination values, and MW combination values. In thatrespect, see for example equations (22) and (26).

In one embodiment, the combination values computing unit 40 isconfigured for computing the ionospheric code minus ionospheric phasecombination values, and the MW combination values. In that respect, seefor example equations (23) and (26).

As mentioned above, the apparatus 100 generating the correctioninformation need not necessarily be the NSS receiver initially obtainingthe raw observations. In FIG. 11 a, a system according to one embodimentof the invention is schematically illustrated wherein a NSS receiverobtains raw observations and transfers those to the apparatus 100.Apparatus 100 then receives the raw observations (i.e., step s10 asdescribed with reference to FIG. 1 a) and then, after processing (stepss20 to s50 as described with reference to FIG. 1 a), sends the generatedcorrection information to the NSS receiver. In the system of FIG. 11 a,the calibration process is therefore performed individually, i.e. on aper receiver basis.

In contrast, FIG. 11 b schematically illustrates a system in oneembodiment of the invention wherein apparatus 100 broadcasts thegenerated correction information to more than one NSS receiver (of thesame or similar type) based on the raw observations received from onesingle NSS receiver.

FIG. 11 c schematically illustrates a system in one embodiment of theinvention, which differs from the system of FIG. 11 b in that thegenerated correction information is not transferred to the NSS receiverfrom which the raw observations originate.

FIG. 11 d schematically illustrates a system in one embodiment of theinvention, in which the apparatus 100 generating the correctioninformation is, or is integrated with, the NSS receiver initiallyobtaining the raw observations. The generated correction information isthen broadcast to more than one NSS receiver.

FIG. 11 e schematically illustrates a system in one embodiment of theinvention, in which the apparatus 100 generating the correctioninformation is, or is integrated with, the NSS receiver initiallyobtaining the raw observations. The generated correction information isthen used by that NSS receiver, without being broadcast to other NSSreceivers.

For the sake of conciseness, FIGS. 11 a to 11 e do not show the precisesatellite information (or information derived therefrom) being receivedby apparatus 100.

For transferring the correction information (as occurring in FIGS. 11 ato 11 d), any suitable format may be used. Further, the correctioninformation may be transferred, for example, in at least one of: (i) acontinuous stream, (ii) together with an update of the receiver firmwareand/or software, and (iii) as stored on the receiver at the time ofmanufacture.

F. Additional Remarks

Any of the above-described methods and their embodiments may beimplemented, at least partially, by means of a computer program. Thecomputer program may be loaded on an apparatus, a rover, a receiver or anetwork station as described above. Therefore, the invention alsorelates to a computer program, which, when carried out on an apparatus,a rover, a receiver or a network station as described above, carries outany one of the above-described methods and their embodiments.

The invention also relates to a computer-readable medium or acomputer-program product including the above-mentioned computer program.The computer-readable medium or computer-program product may forinstance be a magnetic tape, an optical memory disk, a magnetic disk, amagneto-optical disk, a CD ROM, a DVD, a CD, a flash memory unit or thelike, wherein the computer program is permanently or temporarily stored.The invention also relates to a computer-readable medium (or to acomputer-program product) having computer-executable instructions forcarrying out any one of the methods of the invention.

The invention also relates to a firmware update adapted to be installedon receivers already in the field, i.e. a computer program which isdelivered to the field as a computer program product. This applies toeach of the above-described methods and apparatuses.

GNSS receivers may include an antenna, configured to receive the signalsat the frequencies broadcasted by the satellites, processor units, oneor more accurate clocks (such as crystal oscillators), one or morecentral processing units (CPU), one or more memory units (RAM, ROM,flash memory, or the like), and a display for displaying positioninformation to a user.

Where the terms “raw observations receiving unit”, “precise satelliteinformation obtaining unit”, “ambiguities estimating unit”, “combinationvalues computing unit”, “correction information generating unit” and thelike are used herein as units (or sub-units) of an apparatus (such as aGNSS receiver), no restriction is made regarding how distributed theconstituent parts of a unit (or sub-unit) may be. That is, theconstituent parts of a unit (or sub-unit) may be distributed indifferent software or hardware components or devices for bringing aboutthe intended function. Furthermore, the units may be gathered togetherfor performing their functions by means of a combined, single unit (orsub-unit).

The above-mentioned units and sub-units may be implemented usinghardware, software, a combination of hardware and software,pre-programmed ASICs (application-specific integrated circuit), etc. Aunit may include a central processing unit (CPU), a storage unit,input/output (I/O) units, network connection devices, etc.

Although the present invention has been described on the basis ofdetailed examples, the detailed examples only serve to provide theskilled person with a better understanding, and are not intended tolimit the scope of the invention. The scope of the invention is muchrather defined by the appended claims.

The invention also relates to the following embodiments E1 to E16:

-   E1. Method according to any one of the method claims, wherein, when    obtaining (s20) the precise satellite information, information on:    -   (iv) a precise ionosphere model    -   is also obtained.-   E2. Method according to any one of the method claims, or embodiment    E1, wherein, when obtaining (s20) the precise satellite information,    information on:    -   (v) a precise troposphere model is also obtained.-   E3. Apparatus (100) according to claim 12, wherein the raw    observations receiving unit (10) is configured for:    -   receiving raw observations obtained by one of the at least one        NSS receiver observing NSS multiple frequency signals from a        plurality of NSS satellites over at least one day.-   E4. Apparatus (100) according to claim 12 or embodiment E3, wherein    the precise satellite information obtaining unit (20) is further    configured for obtaining information on:    -   (iv) a precise ionosphere model.-   E5. Apparatus (100) according to claim 12 or embodiments E3 or E4,    wherein the precise satellite information obtaining unit (20) is    further configured for obtaining information on:    -   (v) a precise troposphere model.-   E6. Apparatus (100) according to claim 12 or any one of embodiments    E3 to E5, wherein the ambiguities estimating unit (30) is further    configured for setting the ambiguities to integers and resolving    them.-   E7. Apparatus (100) according to claim 12 or any one of embodiments    E3 to E6, wherein the combination values computing unit (40) is    configured for computing multipath combination values of each    frequency.-   E8. Apparatus (100) according to claim 12 or any one of embodiments    E3 to E7, wherein the combination values computing unit (40) is    configured for computing the ionospheric-free code minus    ionospheric-free phase combination values.-   E9. Apparatus (100) according to claim 12 or any one of embodiments    E3 to E8, wherein the combination values computing unit (40) is    configured for computing the ionospheric code minus ionospheric    phase combination values.-   E10. Apparatus (100) according to claim 12 or any one of embodiments    E3 to E9, wherein the combination values computing unit (40) is    configured for computing Melbourne-Wübbena combination values.-   E11. Apparatus (100) according to claim 12 or any one of embodiments    E3 to E10, wherein the combination values computing unit (40) is    configured for computing the ionospheric-free code minus    ionospheric-free phase combination values, and the ionospheric code    minus ionospheric phase combination values.-   E12. Apparatus (100) according to claim 12 or any one of embodiments    E3 to E11, wherein the combination values computing unit (40) is    configured for computing Melbourne-Wübbena combination values and    ionosphere-free code minus ionosphere-free phase combination values.-   E13. Apparatus (100) according to claim 12 or any one of embodiments    E3 to E12, wherein the combination values computing unit (40) is    configured for computing the ionospheric code minus ionospheric    phase combination values, and the Melbourne-Wübbena combination    values.-   E14. Apparatus (100) according to claim 12 or any one of embodiments    E3 to E13, wherein the correction information generating unit (50)    is configured for generating the correction information per    satellite and frequency and/or per satellite and linear combination    of frequencies, based on the computed combination values.-   E15. Computer program product comprising a computer program    according to claim 15.-   E16. Storage medium storing a computer program according to claim    15.

1. Method for generating correction information associated with at leastone global or regional navigation satellite system receiver, hereinafterabbreviated as NSS receiver, wherein the correction informationcomprises information for correcting pseudorange observations useful fordetermining a position of the at least one NSS receiver, the methodcomprising: receiving raw observations obtained by one of the at leastone NSS receiver absenting NSS multiple frequency signals from aplurality of NSS satellites over multiple epochs; obtaining information,hereinafter referred to as “precise satellite information”, on: (i) theorbit position of each one of the plurality of NSS satellites, (ii) aclock offset of each one of the plurality of NSS satellites, and (iii) aset of biases associated with each one of the plurality of NSSsatellites, or information derived from the precise satelliteinformation; estimating ambiguities in the carrier phase of the receivedraw observations, using the precise satellite information, or using theinformation derived from the precise satellite information; computingcombination values based on the received raw observations together withthe estimated ambiguities, to cancel out the effects of the satellitemotion relative to the at least one NSS receiver, the effects of theclocks, the effects of the troposphere and the effects of theionosphere; and generating the correction information per satellite,based on the computed combination values.
 2. Method of claim 1, whereinthe step of receiving raw observations comprises: receiving rawobservations obtained by one of the at least one NSS receiver observingNSS multiple frequency signals from a plurality of NSS satellites overat least one day.
 3. Method of claim 1, wherein the step of estimatingambiguities in the carrier phase of the received raw observations, usingthe precise satellite information, or using the information derivedtherefrom, comprises: setting the ambiguities to integers and resolvingthem.
 4. Method of claim 1, wherein the step of computing combinationvalues comprises computing multipath combination values of eachfrequency.
 5. Method of claim 1, wherein the step of computingcombination values comprises computing ionospheric-free code minusionospheric-free phase combination values.
 6. Method of claim 1, whereinthe step of computing combination values comprises computing ionosphericcode minus ionospheric phase combination values.
 7. Method of claim 1,wherein the step of computing combination values comprises computingMelbourne-Wübbena combination values.
 8. Method of claim 1, wherein thestep of computing combination values comprises computingionospheric-free code minus ionospheric-free phase combination values,and ionospheric code minus ionospheric phase combination values. 9.Method of claim 1, wherein the step of computing combination valuescomprises computing Melbourne-Wübbena combination values andionosphere-free code minus ionosphere-free phase combination values. 10.Method of claim 1, wherein the step of computing combination valuescomprises computing ionospheric code minus ionospheric phase combinationvalues and Melbourne-Wübbena combination values.
 11. Method of claim 1,wherein the step of generating comprises generating the correctioninformation per satellite and frequency and/or per satellite and linearcombination of frequencies, based on the computed combination values.12. Apparatus configured for generating correction informationassociated with at least one global or regional navigation satellitesystem receiver, hereinafter abbreviated as NSS receiver, wherein thecorrection information comprises information for correcting pseudorangeobservations useful for determining a position of the at least one NSSreceiver, the apparatus comprising: a first unit, hereinafter referredto as “raw observations receiving unit”, configured for receiving rawobservations obtained by one of the at least one NSS receiver observingNSS multiple frequency signals from a plurality of NSS satellites overmultiple epochs; a second unit, hereinafter referred to as “precisesatellite information obtaining unit”, configured for obtaininginformation, hereinafter referred to as “precise satellite information”,on: (i) the orbit position of each one of the plurality of NSSsatellites, (ii) a clock offset of each one of the plurality of NSSsatellites, and (iii) a set of biases associated with each one of theplurality of NSS satellites, or information derived from the precisesatellite information; a third unit, hereinafter referred to as“ambiguities estimating unit”, configured for estimating ambiguities inthe carrier phase of the received raw observations, using the precisesatellite information, or using the information derived from the precisesatellite information; a fourth unit, hereinafter referred to as“combination values computing unit”, configured for computingcombination values based on the received raw observations together withthe estimated ambiguities, to cancel out the effects of the satellitemotion relative to the at least one NSS receiver, the effects of theclocks, the effects of the troposphere and the effects of theionosphere; and a fifth unit, hereinafter referred to as “correctioninformation generating unit”, configured for generating the correctioninformation per satellite, based on the computed combination values. 13.NSS receiver comprising an apparatus according to claim
 12. 14. Networknode comprising an apparatus according to claim 12, and furtherconfigured for transferring the generated correction information to atleast one NSS receiver.
 15. Computer program comprising instructionsconfigured, when executed on a computer, to carry out a method accordingto claim 1.